## 1. Introduction

Cognitive radio (CR) is a new approach for wireless communication systems to utilize the existing spectrum resources efficiently. Spectrum utilization can be increased by opportunistically allowing the unlicensed secondary user (SU) to utilize a licensed band in the absence of the primary user (PU) [1–4]. The ability of providing awareness about the usage of the frequency spectrum or the detection of the PU in a desired frequency band lets the SU access the radio communication channel without causing harmful interference to the PU [5–8].

Cooperative wireless communications, which depend on cooperation among distributed single‐antenna wireless nodes, have emerged recently as an alternative to multi‐antenna systems to obtain spatial diversity [9–13]. In a wireless communication system, when the source terminal does not have a good‐enough link with the destination one, cooperative relaying can be utilized to improve spectral efficiency, combat with the effects of the channel fading and to increase the channel capacity. There are various cooperative relaying schemes and two of the most widely studied in the literature are amplify‐and‐forward (AF) and decode‐and‐forward (DF) protocols. Between them, the DF cooperation protocol is considered in this chapter, in which the relay terminal decodes its received signal and then re‐encodes it before transmission to the destination [14]. In order to achieve higher outage performance, we investigate the DF relaying in CR networks over Rayleigh fading channels, subject to the relay location for a SU. Then, we obtain the optimal relay location for the CR networks and optimal transmission rate of the SU using the differential evolution (DE) optimization algorithm [15–17].

Most of the previous publications have studied the performance of cooperative communications techniques over different fading channels and under different constraints [18–26]. In [18], the authors derive the analytical error rate expressions to develop power allocation, relay selection and placements with generic noise and interference in a cooperative diversity system employing AF relaying under Rayleigh fading. Woong and Liuqing [19] address the resource allocation problem in a differentially modulated relay network scenario. It is shown to achieve the optimal energy distribution and to find optimal relay location while minimizing the average symbol error rate. The effect of the relay position on the end‐to‐end bit error rate (BER) performance is studied in [20]. Furthermore, Refs. [21–26] investigate the relay node placements minimizing the outage probability where the performance improvement is quantified. Although cooperative transmissions have greatly been considered in the above manuscripts, to the best of the our knowledge, there has not been any notable research for the relay‐assisted CR networks based on the DE optimization algorithm. As far as we know, DE optimization algorithm has not been applied for obtaining the optimal location of the relaying terminal in CR networks over Rayleigh fading channels.

In summary, to fill the above‐mentioned research gap, we here provide an optimization analysis yielding the optimal location of the relaying terminal for the SU in CR networks. Furthermore, we analyse the transmission rate for the SU over Rayleigh fading channels using DE optimization algorithm. As far as we know, DE optimization algorithm has not been applied for obtaining the optimal location of the relaying terminal and the transmission rate in CR networks over Rayleigh fading channels.

The rest of the chapter is organized as follows: the system model and performance analysis are described in Section 2 presenting the relay‐assisted underlay cognitive radio networks. The numerical results and simulations are discussed in Section 3 with the DE optimization approach. Finally, Section 4 provides the concluding remarks.

## 2. System model and performance analysis

This section presents the system model for the CR networks with DF cooperative relaying protocol shown in **Figure 1**. We consider the method developed in [27] that the transmission links between the source‐to‐relay and relay‐to‐destination are subject to Rayleigh fading. In the system model for the cooperative relaying, we have both

where the cosine theorem is used. Here,

In a cognitive radio network, the transmission of a primary user has to be protected from the interference caused by either a secondary user or a relay. The level of the interference induced on the primary user

Here, we consider the worst case channel conditions, namely, Rayleigh fading, might cause some signal power loss between the

respectively [27]. Here,

In this study, it is aimed to minimize the outage probability of the secondary user for the DF relaying scheme and to maximize the transmission rate,

(4) |

where

Here, the outage probability for the secondary user is given by

For the optimization problem, a function is employed to minimize the outage probability and maximize the transmission rate for the DF relay‐assisted CR system. DE optimization algorithm results show that the system performance can be significantly improved for the optimal value of the system parameters, seen in the following section.

## 3. Numerical results and simulations

In this section, the numerical results are illustrated through the performance analysis curves of the proposed underlay cognitive radio networks with DF relaying. The detailed optimization results with the DE algorithm for DF relaying scheme are listed in **Table 1**. Here, the results for the optimal transmission distances, between secondary user source to relay

The outage probability
**Figure 2** with varying
**Figure 2** that the optimal

**Figure 3** shows the transmission rate over Rayleigh fading channel versus

The transmission rate
**Figure 4** when
**Figure 4** indicates that the maximum transmission rate is achieved when the optimal transmission distances are used.

**Figure 5** depicts the outage probability performance as a function of
**Figure 4** closely match with the results in **Figure 5**. Therefore, it can be deduced that the optimal placement of the relay terminal can be performed based on

In **Figure 6**, the transmission rate for the
**Figure 7** using the same parameters in **Figure 6**.

The normalized
**Figure 8**. Besides, in **Figure 9**,

The maximum transmission rate varying with different
**Figure 10**. The figure demonstrates the effect of

Finally, the maximum transmission rate, varying with the normalized distance for different
**Figure 11**. It is seen that while the

## 4. Conclusions

In this chapter, we present a comprehensive performance analysis of the outage probability